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Random matrices are used to filter the center of gravity (CoG) and the covariance matrix of measurements. However, these quantities do not always correspond directly to the position and the extent of the object, e.g. when a lidar sensor is used.In this paper, we propose a Gaussian processes regression model (GPRM) to predict the position and extension of the object from the filtered CoG and covariance matrix of the measurements. Training data for the GPRM are generated by a sampling method and a virtual measurement model (VMM). The VMM is a function that generates artificial measurements using ray tracing and allows us to obtain the CoG and covariance matrix that any object would cause. This enables the GPRM to be trained without real data but still be applied to real data due to the precise modeling in the VMM. The results show an accurate extension estimation as long as the reality behaves like the modeling and e.g. lidar measurements only occur on the side facing the sensor.

Extended Target Tracking With a Lidar Sensor Using Random Matrices and a Virtual Measurement Model
(2022)

Random matrices are widely used to estimate the extent of an elliptically contoured object. Usually, it is assumed that the measurements follow a normal distribution, with its standard deviation being proportional to the object’s extent. However, the random matrix approach can filter the center of gravity and the covariance matrix of measurements independently of the measurement model. This work considers the whole chain from data acquisition to the linear Kalman Filter with extension estimation as a reference plant. The input is the (unknown) ground truth (position and extent). The output is the filtered center of gravity and the filtered covariance matrix of the measurement distribution. A virtual measurement model emulates the behavior of the reference plant. The input of the virtual measurement model is adapted using the proposed algorithm until the output parameters of the virtual measurement model match the result of the reference plant. After the adaptation, the input to the virtual measurement model is considered an estimation for position and extent. The main contribution of this paper is the reference model concept and an adaptation algorithm to optimize the input of the virtual measurement model.

Multi-object tracking filters require a birth density to detect new objects from measurement data. If the initial positions of new objects are unknown, it may be useful to choose an adaptive birth density. In this paper, a circular birth density is proposed, which is placed like a band around the surveillance area. This allows for 360° coverage. The birth density is described in polar coordinates and considers all point-symmetric quantities such as radius, radial velocity and tangential velocity of objects entering the surveillance area. Since it is assumed that these quantities are unknown and may vary between different targets, detected trajectories, and in particular their initial states, are used to estimate the distribution of initial states. The adapted birth density is approximated as a Gaussian mixture, so that it can be used for filters operating on Cartesian coordinates.

Virtual measurement models (VMM) can be used to generate artificial measurements and emulate complex sensor models such as Lidar. The input of the VMM is an estimation and the output is the set of measurements this estimation would cause. A Kalman filter with extension estimation based on random matrices is used to filter mean and covariance of the real measurements. If these match the mean and covariance of the artificial measurements, then the given estimation is appropriate. The optimal input of the VMM is found using an adaptation algorithm. In this paper, the VMM approach is expanded for multi-extended object tracking where objects can be occluded and are only partially visible. The occlusion can be compensated if the extension estimation is performed for all objects together. The VMM now receives as input an estimation for the multi-object state and the output are the measurements that this multi-object state would cause.

In multi-extended object tracking, parameters (e.g., extent) and trajectory are often determined independently. In this paper, we propose a joint parameter and trajectory (JPT) state and its integration into the Bayesian framework. This allows processing measurements that contain information about parameters and states. Examples of such measurements are bounding boxes given from an image processing algorithm. It is shown that this approach can consider correlations between states and parameters. In this paper, we present the JPT Bernoulli filter. Since parameters and state elements are considered in the weighting of the measurement data assignment hypotheses, the performance is higher than with the conventional Bernoulli filter. The JPT approach can be also used for other Bayes filters.